Abstract : The operation of replenishment at sea is investigated for three supply ships and L combatants using queueing theory concepts and a random walk model in three dimensions. The distribution for total replenishment time given the initial number of combatants to be replenished by each supply ship and a specified cyclic order of replenishment is expressed in terms of its Laplace transform under the assumption of independent, exponential service times for each supply vessel. A method for counting all possible sequences of replenishment is not found, but some preliminary counting techniques are developed which may be useful in its eventual determination. (Author)